The 18-year-old sang Bublé's song 'Home' in front of 12,000 fans after the Canadian singer invited him to the stage.
Leon had bought a ticket for the concert after he was given a masterclass by Bublé on the show.
The Scottish sales assistant admitted that he feels like a winner now whether he comes out on top on the ITV1 singing contest or not.
He said: "It's been the best experience of my whole X Factor journey. If it ended now, I'd still be really happy. It's everyone's dream to play Wembley and now I've done that."
Leon claimed that the experience helped him beat his nerve problem and hopes it will help him get through this week's semi-final show.
He said: "It was just an amazing feeling. I hadn't rehearsed singing the song with Michael but being on stage with him just felt natural.
"I wasn't nervous at all about performing in front of so many people. I loved every minute of it. If I'm ever depressed or low, I'll remember singing with Michael at Wembley and it will cheer me up."
He added: "I think it was because I knew I wasn't getting judged and I could just go up and have fun."
Leon will compete against Rhydian Roberts, Same Difference and Niki Evans on Saturday night to win a place on the final show the following Saturday.